2.1
Using a sheet of graph paper, graph each pair of equations on the same coordinate system. (There should be 2 lines on each graph.) You may use the document link below to help organize your thinking process and for the coordinate planes.
Answer the following questions on your graph paper or on the document you printed and put your work in your classroom binder.
Identify how many intersections are shown on each graph.
Now look at the 2 equations that made the first graph. What is the relationship of their slopes?
Looking at the 2 equations that made the second graph, what is the relationship between their slopes?
Looking at the 2 equations that made the third graph, what is the relationship between their slopes?
On your wikispace, describe the relationship between different pairs of lines and their slopes as it relates to the number of intersections (solutions) that the system of equations will have. Be sure to discuss all 3 graphs and how they are similar or different.
In the first graph there is one solution because the slopes and the y-intercepts are both different. In the second graph there is no solution because the slopes are the same and the y-intercepts are different which tells you that there are no solutions. The third graph has infinite solutions because the equations are exactly the same and have the same slope and y-intercept.
<------------ THE 3 GRAPHS AND TABLES & QUESTIONS W/ ANSWERS
2.2
Describe the 3 different methods for solving (finding a solution) to a system of equations. Why/When would you choose one method over the another? What are you looking for in each system to determine the best method? Discuss any tricks or special techniques to remember when solving each of the methods.
The 3 different methods for solving equations are graphing, combination, and substitution. When I have an equation that has a slope and a fraction I would use the method of graphing. When I have a variable by itself I want to cancel the variable out and so I have can the other one to solve so I would use the method of combination. When the x is on one side of one equation and on the other equation when the y is on one side the you would substitute one of the variables to solve it. With each method I am trying to find the solution of both equations. So when I get the solution I can graph it.
2.3
Look at the graph below. Both functions represent two different bank accounts.
The blue linear function represents a bank account where a person deposited $1000. This person then deposits an additional 100 dollars at the end of each year.
The red linear function represents a bank account where a person deposited $1050. This person then deposits an additional 75 dollars at the end of each year.
Compare and contrast the two bank accounts in your online journal by answering the following questions:
Write a function that represents the red linear function.
What is the y-intercept of each function? Explain in the context of the situation.
What is the slope of each function? Explain in the context of the situation.
Which account is better? Is this always true? Be specific, using dates and account values from the graph to support your argument.
Which account would you choose when opening to save up for your college in a few years and why?
Would you choose that same account to start your child's college fund (if you had a child) and why?
y=100x+1000 is the function for the blue line & y=75x+1050 is the function for the red line.
In the blue line the y-intercept is 1000 because that's how much money i'm started with and that's where is intersects with the y axis. In the red line the y-intercept is 1050 because that's how much money is started with this equation and where it intersects with the y axis.
100x is the slope of the blue line because that is what's making the line go up or down it's what changes the equation. 75x is the slope of the red line because that is what's making the line constant by going up or down.
The blue line account is better because after the 3rd year more money is earned rather than the red line which would be less than the blue line, however this isn't always true because in the first 3 years the red line is earning more money than the blue line.
If I were to open an account for my college fund in a few years I would pick the red line because I would start off with more money in the first few years even though after the first few years i would have less money than the blue line I would actually need more money to start college rather than towards the end of college.
If I were to open an account for my child's college fund I would pick the blue line because over the course of the years when it's time for my child to go to college he/she will have more than if he/she was on the red line account. Also I would want my child to have more money and get into college.
Using a sheet of graph paper, graph each pair of equations on the same coordinate system. (There should be 2 lines on each graph.)
You may use the document link below to help organize your thinking process and for the coordinate planes.
Answer the following questions on your graph paper or on the document you printed and put your work in your classroom binder.
On your wikispace, describe the relationship between different pairs of lines and their slopes as it relates to the number of intersections (solutions) that the system of equations will have. Be sure to discuss all 3 graphs and how they are similar or different.
In the first graph there is one solution because the slopes and the y-intercepts are both different.
In the second graph there is no solution because the slopes are the same and the y-intercepts are different which tells you that there are no solutions.
The third graph has infinite solutions because the equations are exactly the same and have the same slope and y-intercept.
2.2
Describe the 3 different methods for solving (finding a solution) to a system of equations. Why/When would you choose one method over the another? What are you looking for in each system to determine the best method? Discuss any tricks or special techniques to remember when solving each of the methods.
The 3 different methods for solving equations are graphing, combination, and substitution. When I have an equation that has a slope and a fraction I would use the method of graphing. When I have a variable by itself I want to cancel the variable out and so I have can the other one to solve so I would use the method of combination. When the x is on one side of one equation and on the other equation when the y is on one side the you would substitute one of the variables to solve it. With each method I am trying to find the solution of both equations. So when I get the solution I can graph it.
2.3
Look at the graph below. Both functions represent two different bank accounts.
The blue linear function represents a bank account where a person deposited $1000. This person then deposits an additional 100 dollars at the end of each year.
The red linear function represents a bank account where a person deposited $1050. This person then deposits an additional 75 dollars at the end of each year.
Compare and contrast the two bank accounts in your online journal by answering the following questions: